SMOOTHING OF SEMISTABLE FANO VARIETIES

Shentu, Junchao

doi:info:doi/10.18910/76676

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タイトル	SMOOTHING OF SEMISTABLE FANO VARIETIES
著者	Shentu, Junchao Shentu, Junchao
抄録	In this paper we study the smoothing of a semistable Fano variety over a perfect field k. In characteristic 0, the reduced semistable Fano degenerate fibers of Mori fibrations are classified. In positive characteristic, under a suitable W₂ lifting assumption, we prove that a semistable Fano variety always appears as a degenerate fiber in a semistable family if it has a global log structure (in the sense of Fontaine-Illusie-Kato) of semistable type. A geometric criterion for the existence of a log structure of semistable type is given.
公開者	Osaka University and Osaka City University, Departments of Mathematics
掲載誌名	Osaka Journal of Mathematics
巻	57
号	3
開始ページ	617
終了ページ	645
刊行年月	2020-07
ISSN	00306126
NCID	AA00765910
URL	http://hdl.handle.net/11094/76676
言語	英語
DOI	info:doi/10.18910/76676
カテゴリ	紀要論文 Departmental Bulletin Paper
カテゴリ	Osaka Journal of Mathematics / Volume 57, Number 3 （2020-7）

著者版フラグ	publisher
NII資源タイプ	紀要論文
ローカル資源タイプ	紀要論文
dcmi資源タイプ	text
DCTERMS.bibliographicCitation	Osaka Journal of Mathematics.57(3) P.617-P.645
DC.title	SMOOTHING OF SEMISTABLE FANO VARIETIES
DC.creator	Shentu, Junchao
DC.publisher	Osaka University and Osaka City University, Departments of Mathematics
DC.language" scheme="DCTERMS.RFC1766	英語
DCTERMS.issued" scheme="DCTERMS.W3CDTF	2020-07
DC.identifier" scheme="DCTERMS.URI	http://hdl.handle.net/11094/76676
DCTERMS.abstract	In this paper we study the smoothing of a semistable Fano variety over a perfect field k. In characteristic 0, the reduced semistable Fano degenerate fibers of Mori fibrations are classified. In positive characteristic, under a suitable W₂ lifting assumption, we prove that a semistable Fano variety always appears as a degenerate fiber in a semistable family if it has a global log structure (in the sense of Fontaine-Illusie-Kato) of semistable type. A geometric criterion for the existence of a log structure of semistable type is given.
DC.identifier	info:doi/10.18910/76676
citation_title	SMOOTHING OF SEMISTABLE FANO VARIETIES
citation_author	Shentu, Junchao
citation_publisher	Osaka University and Osaka City University, Departments of Mathematics
citation_language	英語
citation_date	2020-07
citation_journal_title	Osaka Journal of Mathematics
citation_volume	57
citation_issue	3
citation_firstpage	617
citation_lastpage	645
citation_issn	00306126
citation_public_url	http://hdl.handle.net/11094/76676
citation_doi	info:doi/10.18910/76676

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